Aircraft: COMMERCIAL FIXED WING
Phase of flight: Initial Approach
Anomaly: ATC Issue All Types; Deviation / Discrepancy - Procedural FAR; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter VFR In IMC; Inflight Event / Encounter Weather / Turbulence

During a flight from to MYAM (to pick up passengers at MYAM); we were forced to climb in Instrument Meteorological Conditions (IMC) without ATC contact.At approximately XA:30 we were flying GPS direct to MYAM and Nassau Approach (121.00) cleared us to descend from 9;000 feet to 2;000 feet. They were experiencing radar shortages at the time and asked us to report 7;000 feet and 6;000 feet which we did. While in the descent I asked Nassau Approach what our missed approach instructions were. Nassau's response was 'cancel IFR on Nassau Radio: 128.00.' I reiterated that I needed instructions if we did not have the airport in sight (MYAM is VFR only and has no approaches) and Nassau Approach came back with the same response: 'cancel on 128.00.' Passing through approximately 3;000 ft and in IMC and rain; I again asked Nassau again what our missed instructions might be if we didn't not see the airport. We got no response. We leveled at 2;000 feet MSL; about the same time we overflew MYAM airport and could not get the field in sight. I decided to remain on my assigned heading and altitude and asked Nassau Approach for missed instructions but heard no response. We continued on our heading (280) and altitude (2;000 feet) for another ten miles (now over open water) making three more attempts to contact Nassau Approach; to which we had no success. I next contacted Nassau Radio on 128.00 and advised them that I did not get the airport in sight and was trying to reach approach. Nassau Radio responded that she understood and wanted to know our intentions. I asked for a turn back to the airport and remain at 2;000 feet as the clouds appeared to be lifting. Nassau Radio responded that heading and altitude where my discretion and keep her advised. We then turned back due East; GPS direct to MYAM making advisory calls on both Nassau Radio and UNICOM. However; 5 miles east of the airport; the ceilings came down and we overflew the airport again in IMC and light rain. Passing the MYAM airport; I called Nassau Radio again and asked them for instructions to climb and for a heading. We received no response. I then called Nassau Approach requesting instructions and also received no response. I tried both frequencies again twice while also making position reports on UNICOM and could hear no response from anyone. We were now over open water and still in IMC conditions; flying East-bound at 2;000 feet; I elected to climb to the last known VFR conditions (7;000 feet) on the eastbound heading and attempt to get back into contact with ATC. In the climb; we made calls to Nassau on 121.00 (the last frequency we had contact with them) at 1;000 foot intervals reading altitude and heading without receiving any response. Finally at 7;000 feet; and now above the overcast layer and in good VMC conditions; Nassau Approach responded to our call; asking if we were looking for an IFR clearance. I responded that I could not get MYAM in sight and needed vectors as I was still IFR. Nassau switched us over to Miami Center without issuing any heading or altitude instructions. Once in contact with Miami Center; we were re-established in radar contact and were given a heading and told to maintain 7;000 feet. The rest of the flight was uneventful. After getting holding instructions over the airport and delaying for about 30 minutes; we made a successful approach resulting in a VFR landing. Air carrier flight crew experienced IMC conditions at a VFR only airport. ATC coordination was problematical.